Algebras of unbounded operators over the ring of measurable functions and their derivations and automorphisms

Authors

  • S. Albeverio Institut fur Angewandte Mathematik, Universitat Bonn, Wegelerstr. 6, D--53115, Bonn, Germany; SFB 611, Bonn, Germany; BiBoS, Bielefeld, Germany; CERFIM, Locarno and USI, Switzerland
  • Sh. A. Ayupov Institute of Mathematics and Information Technologies, Uzbekistan Academy of Sciences, 29 F. Hodjaev str., Tashkent, 100125, Uzbekistan
  • A. A. Zaitov Institute of Mathematics and Information Technologies, Uzbekistan Academy of Sciences, 29 F. Hodjaev str., Tashkent, 100125, Uzbekistan
  • J. E. Ruziev Institute of Mathematics and Information Technologies, Uzbekistan Academy of Sciences, 29 F. Hodjaev str., Tashkent, 100125, Uzbekistan 

DOI:

Keywords:

Kaplansky-Hilbert module, $L^0$-linear operator, unbounded operator, O*-algebra, automorphism, derivation

Abstract

In the present paper derivations and $*$-automorphisms of algebras of unbounded operators over the ring of measurable functions are investigated and it is shown that all $L^0$-linear derivations and $L^{0}$-linear $*$-automorphisms are inner. Moreover, it is proved that each $L^0$-linear automorphism of the algebra of all linear operators on a $bo$-dense submodule of a Kaplansky-Hilbert module over the ring of measurable functions is spatial.

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Published

2009-06-25

Issue

Vol. 15 No. 2 (2009)

Section

Articles

How to Cite

Albeverio, S., et al. “Algebras of Unbounded Operators over the Ring of Measurable Functions and Their Derivations and Automorphisms”. Methods of Functional Analysis and Topology, vol. 15, no. 2, June 2009, pp. 177-8, https://zen.imath.kiev.ua/index.php/mfat/article/view/417.